Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
A) 2.82
B) 2.72
C) 1.82
D) 1.72
E) 0.82

Sum of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:

1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.

Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5

Product of all proper fractions in the form y/(y+1), where y is a positive digit:

1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.

Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7

Closest is 1.72

Answer (D).

x and y are positive digits (1 to 9).


Sent from my iPhone using GMAT Club Forum mobile app

0 is neither positive nor negative. So we can exclude that since we are considering positive digits.

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